Structural Diversity in the Self‐Assembly of Pseudopeptidic Macrocycles

The self‐assembling abilities of several pseudopeptidic macrocycles have been thoroughly studied both in the solid (SEM, TEM, FTIR) and in solution (NMR, UV, CD, FTIR) states. Detailed microscopy revealed large differences in the morphology of the self‐assembling micro/nanostructures depending on the macrocyclic chemical structures. Self‐assembly was triggered by the presence of additional methylene groups or by changing from para to meta geometry of the aromatic phenylene backbone moiety. More interestingly, the nature of the side chain also plays a fundamental role in some of the obtained nanostructures, thus producing structures from long fibers to hollow spheres. These nanostructures were obtained in different solvents and on different surfaces, thus implying that the chemical information for the self‐assembly is contained in the molecular structure. Dilution NMR studies (chemical shift and self‐diffusion rates) suggest the formation of incipient aggregates in solution by a combination of hydrogen‐bonding and π–π interactions, thus implicating amide and aryl groups, respectively. Electronic spectroscopy further supports the π–π interactions because the compounds that lead to fibers show large hypochromic shifts in the UV spectra. Moreover, the fiber‐forming macrocycles also showed a more intense CD signature. The hydrogen‐bonding interactions within the nanostructures were also characterized by attenuated total‐reflectance FTIR spectroscopy, which allowed us to monitor the complete transition from the solution to the dried nanostructure. Overall, we concluded that the self‐assembly of this family of pseudopeptidic macrocycles is dictated by a synergic action of hydrogen‐bonding and π–π interactions. The feasibility and geometrical disposition of these interactions finally render a hierarchical organization, which has been rationalized with a proposal of a model. The understanding of the process at the molecular level has allowed us to prepare hybrid soft materials.     

Engineering Homochiral Metal–Organic Frameworks by Spatially Separating 1D Chiral Metal–Peptide Ladders: Tuning the Pore Size for Enantioselective Adsorption

The reaction of the chiral dipeptide glycyl‐L(S)‐glutamate with Co^II ions produces chiral ladders that can be used as rigid 1D building units. Spatial separation of these building units with linkers of different lengths allows the engineering of homochiral porous MOFs with enhanced pore sizes, pore volumes, and surface areas. This strategy enables the synthesis of a family of isoreticular MOFs, in which the pore size dictates the enantioselective adsorption of chiral molecules (in terms of their size and enantiomeric excess).     

Semidefinite and linear programming integrality gaps for scheduling identical machines

Sherali and Adams (SIAM J Discrete Math 3:411–430, 1990) and Lovász and Schrijver (SIAM J Optim 1:166–190, 1991) developed systematic procedures to construct the hierarchies of relaxations known as lift-and-project methods. They have been proven to be a strong tool for developing approximation algorithms, matching the best relaxations known for problems like Max-Cut and Sparsest-Cut. In this work we provide lower bounds for these hierarchies when applied over the configuration LP for the problem of scheduling identical machines to minimize the makespan. First we show that the configuration LP has an integrality gap of at least 1024/1023 by providing a family of instances with 15 different job sizes. Then we show that for any integer n there is an instance with n jobs in this family such that after \(\varOmega (n)\) rounds of the Sherali–Adams (\(\text {SA}\)) or the Lovász–Schrijver (\(\text {LS}_+\)) hierarchy the integrality gap remains at least 1024/1023.     

Vacancy formation and CO adsorption on gold-doped ceria surfaces

We study the effect of gold doping on oxygen vacancy formation and CO adsorption on the (1 1 0) and (1 0 0) surfaces of ceria by using density functional theory, corrected for on-site Coulomb interactions (DFT + U). The Au dopant substitutes a Ce atom in the surface layer, leading to strong structural distortions. The formation of one oxygen vacancy near a dopant atom is energetically “downhill” while the formation of a second vacancy around the same dopant requires energy. When the surface is in equilibrium with gaseous oxygen at 1 atm and room temperature there is a 0.4 probability that no oxygen atom left the neighborhood of a dopant. This means that the sites where the dopant has not lost oxygen are very active in oxidation reactions. Above 400 K almost all dopants have an oxygen vacancy next to them and an oxidation reaction in such a system takes place by creating a second vacancy. The energy required to form a second vacancy is smaller on (1 1 0) than on (1 0 0). On the (1 1 0) surface, it is much easier to form a second vacancy on the doped surface than the first vacancy on the undoped surface. The energy required to form a second oxygen vacancy on (1 0 0) is comparable to that of forming the first vacancy on the undoped surface. Thus doping makes the (1 1 0) surface a better oxidant but it has a small effect on the oxidative power of the (1 0 0) surface. On the (1 1 0) surface CO adsorption results in formation of a carbonate-like structure, similar to the undoped surface, while on the (1 0 0) surface direct formation of CO₂ is observed, in contrast to the undoped surface. The Au dopant weakens the bond of the surrounding oxygen atoms to the oxide making it a better oxidant, facilitating CO oxidation.     

Dynamics of three coupled limit cycle oscillators with application to artificial intelligence

We study a system of three limit cycle oscillators which exhibits two stable steady states. The system is modeled by both phase-only oscillators and by van der Pol oscillators. We obtain and compare the existence, stability and bifurcation of the steady states in these two models. This work is motivated by application to the design of a machine which can make decisions by identifying a given initial condition with its associated steady state.     

Asymptotic behavior of reaction–advection–diffusion population models with Allee effect

In this work, a qualitative analysis is carried out for reaction–advection–diffusion (RAD) systems modeling the interactions between two species with Allee effect. In particular, we study different scenarios: mutualism, competition, and a predator–prey relationship in order to investigate the survival or extinction of both populations. Global existence and uniqueness of positive solutions of the proposed RAD problems are demonstrated. Equilibrium states and asymptotic behavior of solutions are obtained using the monotone method and the upper and lower solutions technique. Numerical simulations by a Crank–Nicolson monotone iterative method of the different asymptotic solution dynamics are shown to illustrate our theoretical results.     

From Salts to Ionic Liquids by Systematic Structural Modifications: A Rational Approach Towards the Efficient Modular Synthesis of Enantiopure Imidazolium Salts

This paper reports a simple and robust modular synthetic strategy that leads to a large variety of configurationally and structurally diverse imidazole‐based chiral ionic liquids (CILs) by lipase‐catalyzed resolution. The intimate microscopic interactions of the supramolecular ionic network of these imidazolium chiral salts at the molecular level are investigated both spectroscopically (NMR, FT‐IR‐ATR) and theoretically, and a topological analysis of the experimental electron densities obtained by X‐ray dif fr action of single crystals is performed. Our results support the key role played by the relative configuration of the ‐OR group on the hydrogen‐bonding pattern and its strong influence on the final physical properties of the imidazolium salt. We also obtained a reasonable correlation between the observed melting point and the non‐covalent interactions. The spectroscopic data and the topological analysis reflect the key role played by hydrogen bonds between the OH and imidazolium C2H groups in both cation–anion and cation–cation interactions, with the presence of an OH group leading to an additional inter‐cation interaction. This interaction significantly affects the properties of stereoisomeric salts. Even more interestingly, we also studied the effect of the chirality by comparing enantiopure CILs with their racemic mixtures and found that, with the exception of trans‐Cy6‐OH‐Im‐Bn‐Br, the melting points of the racemic mixtures are higher than those of the corresponding enantiomerically pure forms. For stereoisomeric examples, we have successfully explained the differences in melting temperatures in light of the corresponding structural data. Chirality should therefore be taken into account as a highly attractive design vector in the preparation of ILs with specifically desired properties.     

Simultaneous extraction of tocotrienols and tocopherols from cereals using pressurized liquid extraction prior to LC determination

Tocopherols and tocotrienols have been simultaneously determined in food samples using a rapid and simple analytical method including pressurized liquid extraction (PLE) and LC with electrochemical detection. Separation was carried out on a Phenomenex Synergi 4 μm Hydro‐RP 80A column, using a solution of 2.5 mM acetic acid/sodium acetate in methanol/water (99:1, v/v) as mobile phase at a flow rate of 1.0 mL/min. Column temperature was maintained at 30°C. Detection was performed by coulometric detection at 500 mV except for (β+γ)‐tocotrienol, in wheat and rye samples, which was at +350 mV. A palm oil containing a relatively large amount of γ‐tocotrienol and lower concentrations of α‐ and δ‐tocotrienols and α‐ and γ‐tocopherols was used to provide reference retention times for the tocotrienols. Analyte quantification was performed using the external standard method. The calibration equations of tocopherols were used to quantify both tocopherols and their corresponding tocotrienols. The extraction recoveries obtained using the optimized PLE conditions were in the 80–114% range, with RSDs lower than 15%. The method was successfully applied to the determination of tocotrienols and tocopherols in cereal (wheat, rye, barley, maize and oat) and palm oil samples.     

A role for sulfation-desulfation in the uptake of bisphenol a into breast tumor cells

Bisphenol A (BPA) is a widely used plasticizer whose estrogenic properties may impact hormone-responsive disorders and fetal development. In vivo, BPA appears to have greater activity than is suggested by its estrogen receptor (ER) binding affinity. This may be a result of BPA sulfation/desulfation providing a pathway for selective uptake into hormone-responsive cells. BPA is a substrate for estrogen sulfotransferase, and bisphenol A sulfate (BPAS) and disulfate are substrates for estrone sulfatase. Although the sulfated xenobiotics bind poorly to the ER, both stimulated the growth of receptor-positive breast tumor cells. Treatment of MCF-7 cells with BPAS leads to desulfation and uptake of BPA. No BPAS is found inside the cells. These findings suggest a mechanism for the selective uptake of BPA into cells expressing estrone sulfatase. Therefore, sulfation may increase the estrogenic potential of xenobiotics.